Locator for source of electromagnetic radiation having unknown structure or orientation

ABSTRACT

Apparatus for determining the position of a source of electromagnetic radiation relative to a remote object is disclosed. A multicomponent radiating means of unknown orientation is provided having components centered about the origin of the source. A plurality of electrical signals are applied to the components of the multicomponent source to generate a plurality of electromagnetic fields. The electromagnetic fields are multiplied and thus are distinguishable from one another. A multicomponent receiving means is disposed on the remote object. The multicomponent receiving means is provided with at least three orthogonal components for detecting and measuring components of the electromagnetic fields transmitted from the source. The source and receiving means are adapted for operation at a separation distance sufficient to insure that the far-field components of the electromagnetic fields received by the receiving means are substantially greater in magnitude than the near-field components of the fields received by the receiving means. Analyzing means is associated with the receiver for converting the received components of the electromagnetic fields into source position relative to the remote object, and the relative orientation of the remote object, without a priori knowledge of the orientation of the sensor or the relative orientation of its components. The analyzing means operates open-loop with respect to the source and determines source position orientation with at least one ambiguous combination of orientation or position.

BACKGROUND OF THE INVENTION

This invention relates to determining the position and orientation of aremote object with respect to a reference point; and, more particularly,to radiating an electromagnetic field from the reference point,detecting the field at the remote object and analyzing the detectedfield to determine the position and orientation of the remote object.

The use of orthogonal coils for generating and sensing magnetic fieldsis well known. For example, such apparatus has received wide attentionin the area of mapping magnetic fields to provide a better understandingof their characteristics. If a magnetic field around generating coilscan be very accurately mapped through use of sensing coils, it has alsobeen perceived that it might be possible to determine the location ofthe sensing coils relative to the generating coils based on what issensed. However, a problem associated with doing this is that there ismore than one location and/or orientation within a usual magnetic dipolefield that will provide the same characteristic sensing signals in asensing coil. In order to use a magnetic field for this purpose,additional information must therefore be provided.

One approach to provide the additional information required for thispurpose is to have the generating and sensing coils move with respect toeach other, such as is taught in U.S. Pat. No. 3,644,825. The motion ofthe coils generates changes in the magnetic field, and the resultingsignals then may be used to determine direction of the movement or therelative position of the generating and sensing coils. While such anapproach removes some ambiguity about the position on the basis of thefield sensed, its accuracy is dependent on the relative motion, and itcannot be used at all without the relative motion.

Another approach that has been suggested to provide the additionalrequired information is to make the magnetic field rotate as taught inKalmus, "A New Guiding and Tracking System," IRE Transactions onAerospace and Navigational Electronics, March 1962, pages 7-10. Todetermine the distance between a generating and a sensing coilaccurately, that approach requires that the relative orientation of thecoils be maintained constant. It therefore cannot be used to determineboth the relative translation and relative orientation of the generatingand sensing coils.

U.S. Pat. No. 3,868,565, assigned to the same assignee, teaches atracking system for continuously determining at the origin of areference coordinate system the relative translation and orientation ofa remote object. The tracking system includes radiating and sensingantenna arrays each having three orthogonally positioned loops. Properlycontrolled excitation of the radiating antenna array allows theinstantaneous composite radiated electromagnetic field to be equivalentto that of a single loop antenna oriented in any desired direction.Further control of the excitation causes the radiated field to nutateabout an axis denoted a pointing vector. This tracking system isoperated as a closed-loop system with a computer controlling theradiated-field orientation and interpreting the measurements made at thesensing antenna array. That is, an information feedback loop from thesensing antenna array to the radiating antenna array providesinformation for pointing the nutation axis toward the sensing antennaarray. Accordingly, the pointing vector gives the direction to thesensing antenna array from the radiating antenna array. The properorientation of the pointing vector is necessary for computation of theorientation of the remote object. The signals detected at the sensingantenna include a nutation component. The nutating field produces adifferent nutation component in each of the three detected signals. Theorientation of the sensing antenna array relative to the radiatedsignals is determined from the magnitudes of these components.

U.S. Pat. No. 4,054,881, assigned to the same assignee, teaches amagnetic or near-field non-tracking system for determining, at a remoteobject, the position of the remote object with respect to a referencecoordinate system. The orientation of the remote object can bedetermined, at the remote object, with respect to the referencecoordinate system by using an iterative computational scheme. This isaccomplished by applying electrical signals to each of three mutuallyorthogonal radiating antennas, the electrical signals being multiplexedwith respect to each other and containing information characterizing thepolarity and magnetic moment of the radiated electromagnetic fields. Theradiated fields are detected and measured by three mutually orthogonalreceiving antennas, having a known spatial relationship to the remoteobject, which produces nine parameters. These nine parameters, incombination with one known position or orientation parameter aresufficient to determine the position and orientation parameters of thereceiving antennas with respect to the position and orientation of theradiating antennas.

Copending, allowed, U.S. Patent application, Ser. No. 62,140 filed July30, 1979 entitled REMOTE OBJECT POSITION AND ORIENTATION LOCATER, andassignee to the same assignee; and copending U.S. patent applicationSer. No. 164,783, filed June 30, 1980, entitled REMOTE OBJECT POSITIONAND ORIENTATION LOCATOR and assigned to the same assignee, teach severalimprovements to U.S. Pat. No. 4,054,881. In particular, two mutuallyorthogonal radiating antennas each transmit electromagnetic radiation tothree mutually orthogonal receiving antennas. Alternately, threemutually orthogonal radiating antennas each transmit electromagneticradiation to two mutually orthogonal receiving antennas. The first ofthe above noted applications discloses a near-field system and thesecond of the above noted applications discloses a far-field system.Measurement of the transmitted signals as received by the set oforthogonal receiving antennas produces information which, in combinationwith two known position or orientation parameters, is sufficient todetermine in a non-iterative manner the position and orientation of thereceiving antennas with respect to the position and orientation of theradiating antennas.

Copending, allowed, U.S. Patent application, Ser. No. 954,126, filedOct. 24, 1978, assigned to the same assignee and entitled METHOD ANDAPPARATUS FOR TRACKING OBJECTS, now U.S. Pat. No. 4,298,874, teaches atracking system for: (a) determining at the origin of a first bodycoordinate reference frame the relative position and orientation of asecond body, and (b) determining at the origin of a second bodycoordinate reference frame the relative position and orientation of thefirst body. The separation distance between the bodies is not limited tothe near field. Each body of the tracking system includes at least twoindependently oriented stub dipoles for radiating and sensingelectromagnetic fields. Properly controlled excitation of the radiatingantenna allows the radiated field to nutate about an axis denoted apointing vector. The first body receives radiation transmitted from thesecond body and establishes the pointing angles to the second body withrespect to the first body coordinate reference frame. The processingwhich determines the pointing angles is dependent on the fact that nomodulation or nutation components exist in the radial direction. Thefield received by the first body can include information defining thesecond body's pointing angles to the first body with respect to thesecond body's coordinate reference frame and the relative roll abouttheir mutually aligned pointing axes. This information is sufficient fordetermining the orientation of the first body relative to the second.This process is then repeated with the second body receiving radiationtransmitted from the first body. Further, information can be transmittedfrom the first body to the second body which established a vector fromthe second body to a third body, thus defining the location of the thirdbody at the second body.

However, in the context of a non-tracking far-field system there stillremains a need to determine the position of a source of electromagneticradiation relative to a remote object in the case where the source is ofunknown structure and orientation.

SUMMARY OF THE INVENTION

According to the present invention these and other problems in the priorart are solved by provision of a multicomponent radiating means ofunknown structure and orientation having components centered about theorigin of a source or transmitter. The source includes means forapplying to the plurality of radiating means electrical signals whichgenerate a plurality of electromagnetic fields. The signals areformatted or multiplexed such that the electromagnetic fields aredistinguished from one another. A multicomponent receiving means isdisposed on a remote object. The receiving means is provided with atleast three orthogonal components for detecting and measuring componentsof the electromagnetic fields transmitted by the radiating means. Thethree components of the receiving means are centered about the origin ofa reference coordinate frame associated with the remote object. Theradiating means and receiving means are specifically adapted foroperation at a separation distance sufficient to insure that thefar-field components of the electromagnetic fields received by thereceiving means are substantially greater in magnitude than thenear-field components of the electromgnetic fields received by thereceiving means. Analyzing means is associated with the receiving meansfor converting the received components of the electromagnetic fieldsinto source position relative to the remote object, and the relativeorientation of the remote object, without a priori knowledge of theorientation of the source or the relative orientation of its components.The analyzing means operates open-loop with respect to the radiatingmeans and determines source positon relative to the remote object withat least one ambiguous combination of orientation or position.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a partly block, side elevational view of a landing aid systemin accordance with an embodiment of this invention;

FIG. 2 is a graphical representation showing the relationship betweenelectric field strength and distance from a radiator;

FIG. 3 is a simplified representation of a electric field associatedwith a current-carrying electric dipole;

FIG. 4 is a graphical representation of the location coordinate systemof the remote object with respect to the location of the origin of thereference coordinate frame;

FIG. 5 is a graphical representation of the orientation coordinatesystem of the remote object with respect to the reference coordinateframe;

FIG. 6 is a graphical representation of the amplitude of the signalsapplied to the transmitting antennas, with respect to time, in the casewhere the signals are frequency division multiplexed;

FIG. 7 is a block diagram of a portion of the receiver in accordancewith an embodiment of this invention;

FIG. 8 is a graphical representation of the far-field electromagneticcoupling of a three axis sensor to a three axis source; and

FIG. 9 is a graphical representation of the far-field electromagneticcoupling of a three axis sensor with a three axis source of unknownorientation and structure;

FIG. 10 is a flow chart for the computations carried out in athree-state power solution for remote object position and orientation;

FIG. 11 is a flow chart of the computations carried out in a two-statepower and dot product solution for remote object position andorientation;

FIG. 12 is a graphical representation of the signals applied to thetransmitting antennas, with respect to time, in the case where thesignals are time division multiplexed;

FIG. 13 is a schematic representation of a transmitter employed in atime division multiplexed system;

FIG. 14 is a schematic representation of a transmitter employed in afrequency division multiplexed system.

DESCRIPTION OF THE PREFERRED EMBODIMENTS APPARATUS

The invention is described herein in the context of a system fordetermining the position and orientation of a remote object relative toa source of known structure. When encountering a source of unknownstructure the system is provided with means for determining the positionof the source relative to a reference coordinate frame centered at theremote object.

THREE AXIS TRANSMISSION AND THREE AXIS SENSING WITH FREQUENCY DIVISIONMULTIPLEXING

Although the invention may have utility in a number of environments,only an embodiment relating to a long distance landing system isdescribed in detail. Referring to FIG. 1, a landing aid system 10includes ground based components 30 for radiating an electromagneticfield and airborne components 20 for receiving the electromagnetic fieldand determining the position and orientation of airborne components 20with respect to ground based components 30. Ground based componentsinclude a signal generator 31 coupled in parallel to power amplifiers32, 33 and 34. A ground antenna array 40 includes orthogonal electricdipole antennas 41, 42, and 43 (denoted X, Y, Z) coupled to poweramplifiers 32, 33, and 34, respectively. The dipole antennas 41, 42 and43 are short relative to the wave length of the carrier frequency sothat they each produce an electric dipole-field pattern providingspatial component data unique to each antenna. A monitor receiver 44 iscoupled to signal generator 31, spaced from ground antenna array 40 andhas an orthogonal antenna array 45 for receiving electromagneticradiation from ground antenna array 40. The separation distance ofmonitor receiver 44 from the ground antenna array 40 is such that theelectromagnetic field has a far-field component substantially in excessof the near-field component. Monitor receiver 44 provides a means ofverifying the electromagnetic transmission from ground antenna array 40.Airborne components 20 include a three-axis receiving antenna consistingof mutually orthogonal elements (21, 22 and 23) and analyzing means forconverting the received components of the electromagnetic fields intoremote object position and orientation comprising three identicalchannels of amplification (25, 26 and 27), frequency translation (55, 56and 57), and signal processing (58, 59 and 60). The analyzing means alsoincludes the computer 50 which receives the outputs of the three signalprocessors and calculates position and orientation for display at 51.More specifically, antenna array 21 includes receiving dipole antennas22, 23 and 24 (denoted U, V, W) coupled sequentially to signalamplifiers 25, 26 and 27, respectively, frequency translators 55, 56 and57, respectively, and signal processors 58, 59 and 60 respectively.

Landing aid system 10 operates "open loop" in that the onlycommunication between airborne components 20 and ground based components30 is the radiated electromagnetic field from ground based components30. There need be no communication from airborne components 30 to groundbased components 30 in order to establish the position and orientationof receiving antenna array 21 with respect to ground antenna array 40.Further, landing aid system 10 allows simultaneous use by any number ofremote users. In addition to providing the capability for measuringposition and orientation, the signals radiated by ground antenna array40 can provide a one-way data link from ground based components 30 toreceiving antenna array 21. The link can carry information such astransmitter identification, transmitter power, field distortioncorrections, locations of nearby obstacles, the location of the landingsite relative to ground antenna array 40 and wind direction.

Referring to FIG. 2, the field produced by excitation of a dipoleantenna can be separated into two components referred to as thenear-field and the far-field components. According to the presentinvention, the separation distance of the remote object from thetransmitting means is limited to far-field conditions. The far-fieldcomponent of the transmitted electromagnetic radiation decreaseslinearly as the distance between the remote object and the transmitterincreases. The intensity of the far-field depends on the relative sizeof the antenna and the wave length of the excitation frequency. Forelectrically short antennas, as the wave length of the excitationfrequency is shortened, or the excitation frequency is increased, thestrength of the far-field component increases. The far-field componentof electromagnetic radiation is generally used for long distancecommunications and navigation. On the other hand, the near-fieldcomponent of electromagnetic radiation decreases with the cube of thedistance from the antenna preventing its detection at large distances.The intensity of the near-field is not a function of frequency and itcan be quite high at short distances or low excitation frequencies whichreduce field distortion. When using the far-field component, someadditional field distortion occurs because of surrounding objects. Theamount of distortion resulting from surrounding objects depends on theconductivity and permeability of these objects and their size andlocation relative to the receiving and transmitting antennas. It ispossible to predict and compensate the distortion caused by nearby fixedobjects and hence essentially remove position and orientation errorscaused by these objects.

Ground based components 30 generate a far-field landing aid signal.Signal generator 31 generates the electrical signals which excite eachof antennas 41, 42 and 43. The signal must be multiplexed so receivingantenna array 21 can distinguish the electromagnetic radiation from eachof the antennas 41, 42 and 43. Although the list is not exhaustive, theelectromagnetic radiation transmitted from each of the antennas 41, 42and 43 may be distinguished by using time division multiplexing,frequency multiplexing, phase multiplexing and spread spectrummultiplexing. Additionally, the electrical signal may containinformation characterizing the phase of the electromagnetic radiation. Asimple example would be to include a timing pulse whenever the signalgoes positive. Alternatively, if frequency multiplexing is used, theexcitation to each of antennas 41, 42 and 43 is advantageously coherent.That is, periodically all of the signals go positive simultaneously (seeFIG. 6). Additionally, the data frequency determines the spacing betweenthe carrier frequencies, and is thus the basic reference frequency ofsignal generator 31. The data frequency is labeled f_(o) in FIG. 6.Advantageously, the reference frequency will be derived from atemperature compensated crystal oscillator in the 10 MHz range andfrequency selection will be in 10 kHz steps.

The three power amplifiers 32, 33 and 34 boost the outputs of signalgenerator 31 to a level sufficient to produce the desired power with thegiven antenna. To make efficient use of the power available, a switchingpower amplifier may be used. For example, either class D (carrierfrequency switching) with a class S (high frequency switching) modulatorcan be used. An RFI filter is advantageously also included.

Ground antenna array 40 includes mutually orthogonal dipole antennas 41,42 and 43 and may be located near the landing pad. The relationship ofthe landing pad to ground antenna array 40 can be included in theone-way data stream to airborne components 20. Antenna design in thefar-field context is highly dependent on the operating carrierfrequency. For a long distance landing aid system 10, a carrierfrequency of 220 MHz is appropriate. A dipole antenna whose length isapproximately one-tenth of the wave length of the carrier frequencywould give a dipole length of approximately 12 centimeters.

Monitor receiver 44 is similar to an airborne receiver, but omitsposition/orientation computations, data decoding, and display. Itsfunction is to insure that electromagnetic field amplitudes and phasesradiated from ground antenna array 40 are correct. When deviations arefound, change instuctions are issued to the signal generator. If signalscannot be maintained within prescribed tolerances, the monitor can placean out-of-tolerance message in the data stream. Of course, it can beappreciated that monitor receiver 44 is not necessary to an embodimentof this invention.

Airborne components 20 of landing aid system 10 for a frequency divisionmultiplexing embodiment are shown in FIG. 1 and having a separate signalprocessing path for each of the signals from receiving dipole antennas22, 23 and 24. Although there is additional discussion below of variousmultiplexing alternatives, it can readily be appreciated that if timedivision multiplexing were used, a single path could be switched amongantennas 22, 23 and 24.

FIG. 7 shows a more detailed block diagram of a signal path, inparticular the U antenna signal path. For practical reasons, amplifiergroup 52 and frequency translator group 53 are broken into severalcomponents and spread throughout the signal path. More specifically, Uamplifier 25 of amplifier group 52 includes a preamplifier 61, gaincontrol 63, amplifier 62 and amplifier 64. Frequency translator 55 offrequency translator group 53 includes band pass filters 65 and 65',mixer 66, mixer 67, low pass filter 68 and synthesizer 69. Accordingly,receiving dipole antenna 22 is coupled to preamplifier 61, band passfilter 65, gain control 62, amplifier clipper 63, mixer 66, band passfilter 65, amplifier clipper 64, mixer 67 and low pass filter 68.Synthesizer 69 is connected to mixers 66 and 67. The output of low passfilter 68 is connected to signal processor 58.

Signal processor 58 includes parallel combinations of the sequentialconnection of a mixer, an integrator and a sample-and-hold block. Morespecifically, each of the parallel paths has mixers 70 through 75,integrators 76 through 81 and sample-and-hold blocks 82 through 87. Theoutputs from sample-and-hold blocks 82 through 87 are coupled tocomputer 50 and in turn coupled to display 51. In this embodiment, thereare six parallel paths for processing the signal from the U antenna.There is one path for signals received from the Y transmitting antennareceived by the U receiving antenna, denoted Y/U. Similarly, there isone path for signals received from the X transmitting antenna receivedby the U receiving antenna, denoted X/U. The transmitted signal from Zantenna has two frequencies for carrying a binary code and requires twopaths, denoted Z₁ /U and Z₀ /U. Further, during acquisition twoadditional signals are processed so data transmitted by the Z antenna isnot lost. These signals paths are denoted Z₁ /Uq and Z₀ /Uq and havenegligible output when the receiver is locked on the transmittedfrequencies.

The metal aircraft upon which receiving antenna array 21 is mountedcauses some distortion of the electromagnetic fields received by theantenna. Unless the aircraft is very close to the transmitter, thisdistortion may be described by a linear transformation which maps thefree space fields into three antennas 22, 23 and 24. For example, afield aligned exactly with the length of the aircraft will also appearin the transverse and vertical receiving antennas. This effect isconstant for a given aircraft and installation. It is easily correctedby applying an inverse linear transformation to the measured data.

The input bandwidth of amplifier group 52 is advantageously restrictedto the 219-221 MHz band after which the signals are boosted to asuitable level and noise impulses are clipped. Accurate gain control isused to obtain maximum effectiveness in clipping noise. Alternatively,an impulse detector may be applied at this point to shut off amplifier25 when an impulse occurs. The signal is now translated downward to aconvenient intermediate frequency such as 10 MHz. The bandwidth is alsoreduced to 100 kHz. After the final amplification and clipping, thesignal is translated downward to approximately 100 kHz for finalprocessing.

The mixing frequencies required to accomplish the necessary frequencytranslation are synthesized by standard techniques. The first mixingfrequency is selectable in 10 kHz steps from 209-211 MHz. This allowsany selected signal in the 219-221 MHz band to be translated to 10 MHz.The second mixing frequency of 10.1 MHz is fixed and translates the 10MHz intermediate frequency to the 100 kHz processing frequency. Forinitial acquisition, these frequencies are synthesized from a stablereference oscillator. After acquisition, they can be locked to thereceived signal to remove any frequency error.

Signal processor group 54 must acquire the received signals, establishthe timing reference, make measurements for position/orientationcomputations, and decode transmitted data. To do this, it uses a seriesof phase-locked loops, frequency dividers, and integrators. Interfacewith computer 50 is accomplished by an A/D converter and a suitablebuffer. Signal acquisition is accomplished by the equivalent of a pairof phase-locked loops. In this particular example, as stated, frequencymultiplexing is used and data is carried only by one radiating antenna(the Z signal shown in FIG. 6). The frequencies for carrying data, i.e.ones and zeros, on the Z signal are referred to as the mark and spacefrequencies. Accordingly, the phase-locked loops can operate at, forexample 110 KHz to correspond to the mark and space frequencies of the Zsignal. Loop bandwidth may be changed for initial acquisitions and latertracking, but in either case, it will be sufficiently low to cause theloop to ignore the effects of the frequency shift keying. The 10 kHzreference timing is obtained as the difference between the frequenciesof the two oscillators generating the mark and space frequencies. Actualimplementation can use measurements of both the sine and cosineintegrals for measurement and locking, respectively.

Signal measurements are made by mixing a received signal with a locallygenerated signal and integrating the product. A coherent set of mixingfrequencies (for example, 120, 110, 100, 90 kHz) corresponding to thefour transmitting frequencies is synthesized from the 10 kHz referencefrequency. The Integrators 76-81 are advantageously reset about evey0.001 seconds by the reference signal. The value in each of theintegrators is transferred to sample-and-hold circuits 82-87 just priorto the resetting of integrators 76-81.

Decoding of the data and averaging of the measurements is accomplishedby software. Computer 50 can measure signal amplitude andsignal-to-noise ratio on a sample-by-sample basis. Navigationmeasurements of the X and Y signals are accomplished simply by summingan appropriate number of 0.001 second samples. A similar procedure isused on the Z channel for initial acquisition. When measurementsindicate a satisfactory signal-to-noise ratio, data may be extracted bycomparing the Z-mark samples to the Z-space samples. Z-navigationinformation is based on an average of those samples corresponding to thedata received. That is, only the Z-mark or Z-space sample at a givensampling point is used, depending on the decision about which carrierwas transmitted during that interval.

The computer and display can be common to both long distance landing aidsystem 10 and the landing aid systems disclosed in U.S. Pat. No.4,054,881 to Frederick H. Raab issued Oct. 18, 1977 entitled REMOTEOBJECT POSITION LOCATER and copending application Ser. No. 62,140 filedJuly 30, 1979, to Raab, entitled REMOTE OBJECT POSITION LOCATER, bothassigned to the same assignee. Both the aforementioned patent and patentappliciation are hereby incorporated by reference. This is particularlyadvantageous for reducing cost and for simplification of equipment.Further, an aircraft may use the present long distance landing aidsystem 10 to navigate to within a few kilometers of the landing pointand then acquire signals from the landing aid systems disclosed in theaforementioned patent and application for final approach guidance. Thecomputer and display can be anything suitable and are therefore notdiscussed here in detail.

TWO AXIS TRANSMISSION OR TWO AXIS SENSING WITH FREQUENCY DIVISIONMULTIPLEXING

Although FIGS. 1 and 7 detail a landing aid system 10 utilizing threetransmitting antennas, 41, 42 and 43, and three receiving antennas 22,23 and 24, a landing aid system utilizing two transmitting antennas 41and 42, and three receiving antennas 22, 23 and 24, or a landing aidsystem utilizing three transmitting antennas 41, 42 and 43, and tworeceiving antennas 22 and 23, may be provided. Two axis transmissionwith three axis sensing simplifies the transmitter. This arrangementalso brings about an increase in processing in the case where timedivision multiplexing is used to distinguish the signals applied to eachaxis of the transmitting antenna array. Three axis transmission withthree axis sensing simplifies the receiver. However, the use of twoantennas for either transmitting or receiving does add an additionalambiguity to the system. This can be corrected by, in addition tospecifying that the airplane is flying right-side-up or upside down,specifying that the airplane is approaching the landing site from eitherthe north or south, or the east or west. Apparatus for transmitting withonly two orthogonal antennas is the same as that previously describedwith reference to FIG. 1 except that only two of the X, Y or Z signalspaths are necessary. Apparatus for receiving these signals is the sameas that previously described with reference to FIGS. 1 and 7 except thatthe remaining signal paths contain fewer parallel paths since the signalfrom one of the X, Y or Z transmitting antennas is not present.Apparatus for receiving three transmitted signals with only tworeceiving antennas is the same as that previously described with respectto FIGS. 1 and 7 except that only two signal paths are necessary for thetwo orthogonal receiving antennas.

TIME DIVISION MULTIPLEXING

FIG. 12 depicts a pulsed carrier wave signal format suitable for use ina time division multiplexed system. The three axes of the transmittingantenna are excited sequentially by signals of the same frequency. Thedurations of the three pulses are known (fixed), with the X-axisexcitation pulse longer than the others to allow the receiver toestablish synchronization, thereby knowing which received signals toattribute to which transmitting axis.

To allow rejection of multipath effects, a "dead space" might beinserted between the pulses to allow time for echos to die out. Ifmultipath interference were no problem, all three axes could beexcitated simultaneously by signals of different frequencies or bysignals modulated by different spread spectrum codes. These are ordinaryengineering design decisions that must be made for each application ofthe disclosed concept.

Formats for two-state excitation are similar but simply omit excitationof one axis. If two-axis reception is used, a three-state excitationpattern as described above is still required.

The carrier frequency for these signals would normally be in the rangeof 300 to 3000 MHz with present technology. The excitation pattern couldbe repeated at frequencies in the range of 1 kHz to 30 MHz.

FIG. 13 depicts a block diagram of a transmitter for a time divisionmultiplexed system. Note that for two-state transmission, the Z-axis ofthe antenna and the associated driving circuitry is omitted.

All signals in the transmitter are derived from a stable oscillator 200by a frequency synthesizer 201. The derived radio frequency signals areswitched to the power amplifiers 207, 208, and 209 by gates 203, 204,and 205, which operate under the control of a sequencer 206. The poweramplifiers 207, 208 and 209 produce excitation voltages w_(x), w_(y),and w_(z) as inputs to the antenna axes 210, 211, and 212, respectively.The antennas 210, 211 and 212 are dipoles that are short relative to thewavelength of the carrier frequency so as to produce an electricdipole-field pattern.

A receiver suitable for use in a time division multiplexed system isillustrated in FIG. 14. Signals are received by short dipole antennas213, 214, and 215 and preamplified by preamplifiers 216, 217, and 218.Note that for two-axis reception of three-state transmissions, onereceiving antenna and the associated amplifiers can be omitted.

After preamplification, the three received signals are converted to anintermediate frequency by mixers 219, 220, and 221, which are driven bysignals produced by an oscillator 222, and a synthesizer 223. Note thatall signals and timing in the receiver are derived from one masteroscillator. Not shown is apparatus for phase-locking to the receivedsignal, which may be added and is standard technology.

Intermediate-frequency signals are amplified by amplifiers 224, 225, and226. The amplified intermediate-frequency signals are mixed with signalsof same frequency in mixers 227, 228, and 229. The outputs of thesemixers are integrated by integrators 230, 231, and 232, and sampled by233, 234, and 235; outputs are acquired by the computer 239, whichperforms the required mathematical operations to extract position andorientation information, which is displayed by 240. The mathematicaloperations hereinafter developed are equally applicable to time divisionmultiplexed and frequency division multiplexed signal formats as well asmany other types of signal formats.

OPERATION

Referring now back to the frequency division multiplexing embodimentillustrated in FIGS. 1, 6 and 7, if unambiguous measurements are desiredgeometrical considerations result in inclusion of a timing reference inthe transmitted signal. They also require airborne components 20 tomeasure the signal components induced in each receiving antenna 22, 23and 24 by each transmitting antenna 41, 42 and 43. These requirementsand any additionally desired data transmission form the constraints onsignal format. While any choices are possible, coherent frequencydivision multiplex/frequency shift keying may be suitable for manygeneral purpose users.

It should be noted that in order to facilitate the orderly developmentof a position and orientation finding algorithm, the three transmittingantennas will be designated a three axis source 98, and the threereceiving antennas will be designated a three axis sensor 100. (FIG. 5)

FAR FIELD COUPLING

Excitation of an electric dipole or loop (magnetic dipole) antennaproduces terms that vary as 1/ρ³, 1/ρ², and 1/ρ, which are referred toas quasi-static (near) field, induction field, and far field,respectively. At large distances (ρ>>λ/2π), the far-field terms dominateand the resultant electric and magnetic fields form essentially planewaves. The electric and magnetic field vectors are orthogonal to eachother and both are orthogonal to the direction of propagation. The crossproduct of the electric and magnetic field vectors, called the Poyntingvector, represents power flow, and is oriented in the direction ofpropagation.

It is convenient to think of far-field coupling in terms of the behaviorof electric dipoles, although essentially the same relationships holdfor magnetic dipole (loop) sources and sensors. The electric fieldresulting from the excitation of an electrically short dipole is:

    E.sub.t =(Ilπ/λ.sup.2 ρ)sin δ          (1)

where the excitation current is I cos ωt, the antenna length is l, and λis the wavelength of the carrier frequency. The off-axis angle δ and thefield pattern for each antenna are defined by Equation (1) and are shownin FIG. 3. Note that in contrast to the near-field, the far-fieldintensity varies as the inverse of distance and is frequency dependent.

The magnetic field vector is related to the electric field vector by thefree-space impedance η≃377Ω, thus

    |H|=(|E|/η)        (2)

In the receiving or (or sensing) mode, a dipole has the same pattern asit does in transmitting. An elementary dipole sensor therefore producesan output proportional to the cosine of the angle between the electricfield vector and the dipole axis. Note that variation of the fieldstrength with the sine of the off-axis angle δ is a characteristic ofelementary short dipoles. This simple variation does not apply todipoles whose lengths are a significant portion of a wavelength (0.1λ orgreater) or arrays of coupled colinear elements. For example, the fieldstrength produced by a half-wave dipole varies as cos (π/2 cos δ)/sin δ.

A coordinate system for determination of the position of the receiverrelative to the transmitter is shown in FIG. 4. The X, Y and Z axes arealigned with north, east, and vertical, respectively, and are centeredat the center of transmitting ground antenna array 40. Location ofreceiving antenna array 21 may be specified in either rectangularcoordinates (x, y, z) or in polar coordinates (α,β,ρ). It may also bespecified by the distance ρ and two of the three orientation anglesψ_(x), ψ_(y), or ψ_(z).

Measurement of the three transmitted signals from ground antenna array40 as received by the set of three orthogonal receiving antennas 22, 23and 24 produces nine parameters which are sufficient to determine thesix position and orientation parameters. As noted earlier this assumesone orientation or position parameter is independently determined. Whilethere are a variety of computational algorithms that can be used, it isconceptually easiest to begin by using relative amplitudes to determineposition.

The first step in synthesizing a position and orientation findingalgorithm is the definition of coordinates and vector-matrixformulations relating sensor output to source excitation.

The geometric relationship between the three-axis source 98 and thethree-axis sensor 100 is shown in FIG. 5. The source coordinate frame X₁-Y₁ -Z₁ is defined by the axes of the source 98. Alignment of these axeswith some convenient natural reference such as north, east and down isassumed. The source axes can be effectively aligned with any desiredcoordinate frame by altering the excitation. Similarly, coordinatesmeasured in the source coordinate frame can be converted to any desiredcoordinate frame mathematically.

The sensor position is specified in rectangular (x, y, z) or spherical(α, β, ρ) coordinates defined relative to the source coordinate frame.Sensor orientation is specified by a sequence of three rotations.Azimuthal rotation by ψ first turns the sensor about its Z axis from +Xtoward +Y. The elevation rotation by θ then turns the sensor about its Yaxis from +X to -Z. Finally, a roll rotation by φ turns the sensor aboutits X axis from +Y to +Z. Note that in the zero-orientation condition,the three sensor axes are parallel to the corresponding source axes, andthat the order of the rotations cannot be interchanged without changingthe values of ψ, θ, and φ.

The excitation of a three-axis electric dipole source 98 and theresultant three-axis sensor output are most conveniently described invector notation. The excitation of the source is therefore representedby f₁ =[f_(1x), f_(1y), f_(1z) ]^(T). The lengths of the three dipolesare assumed to be identical, hence f_(1x), f_(1y), and f_(1z) representthe amplitudes of the currents exciting the dipoles of X-axis, Y-axis,and Z-axis orientation, respectively.

Now let the output of a three-axis sensor be similarly represented by f₃=[f_(3x), f_(3y), f_(3z) ]^(T), and consider the coupling between thatsensor and a similarly aligned source f₂. FIG. 8 depicts a three-axissource 102 and a three-axis sensor 100 whose coordinate frames arealigned. Since the sensor 100 is located on the X₂ axis, the sensor 100is in the null of the X₂ dipole, hence the X₂ excitation produces nosensor response on any axis. The source Y₂ axis is parallel to thesensor Y₃ axis, and therefore produces a response in that axis. However,the electric field resulting from Y₂ axis excitation is orthogonal tothe sensor Z₃ axis and hence produces no Z₃ response. Coupling betweenthe source Z₂ excitation and the sensor Y₃ and Z₃ axes is analogous.

If the three-axis source excitation is represented as a vector f₂ andthe three-axis sensor output is similarly represented as a vector f₃,the source-to-sensor coupling can be described by: ##EQU1## The factor Caccounts for excitation and sensing constants common to all axes. Notethat the far-field coupling matrix S (shown above) is degenerate anddiffers from the near-field coupling matrix.

The coupling between a source 98 and sensor 100 of arbitrary positionand orientation (FIG. 5) can be determined by inserting orthogonalrotation matrices into Equation (3). These matrices are based uponposition azimuth and elevation (α and β) and orientation azimuth,elevation, and roll (ψ, θ, and φ), as shown in Table 1. Note that thesubscript defines both the type of transformation and its independentvariable.

                  TABLE 1                                                         ______________________________________                                        Position            Orientation                                               ______________________________________                                        Azimuth rotates X into Y                                                              ##STR1##                                                                                       ##STR2##                                             Ele- vation rotates X into -Z                                                         ##STR3##                                                                                       ##STR4##                                             Roll rotates Y into Z                                                                not applicable                                                                                  ##STR5##                                             Inverses                                                                              ##STR6##                                                              ______________________________________                                    

Consider first the coupling between the source and a zero-orientationsensor (whose output is f₄), located at (α, β, ρ), as shown in FIG. 5.The excitation f₂ of an equivalent source 102 whose X-axis is alignedwith the line connecting the source 98 and sensor 100 can be determinedby rotating the excitation vector of the real source 98 by positionazimuth and elevation, thus ##EQU2## The coupling to a similarly alignedequivalent sensor f₃ then has the same form as Equation (3), i.e., f₃=(C/p) S f₂. The output of the zero-orientation sensor is then found byapplying inverse position rotations, thus ##EQU3## The equivalentsources and sensors used above are listed in Table 2.

                  TABLE 2                                                         ______________________________________                                        SYMBOL  NAME            DEFINITION                                            ______________________________________                                        f.sub.1 Source            --                                                  f.sub.2 Position-frame source                                                                          ##STR7##                                              f.sub.3                                                                               Position-frame sensor                                                                         ##STR8##                                             f.sub.4 Zero-orientation sensor                                                                        ##STR9##                                             f.sub.5 Sensor                                                                                         ##STR10##                                            ______________________________________                                    

Utilizing Table 1 and equations (3) and (4) f₃ can be expanded asfollows: ##EQU4## The row of zeros in Equation (8) implies that nosource excitation can produce a radial (position-frame X₃) component.

A fixed, three-state excitation pattern based upon the source axes isgiven by: ##EQU5## This is the same excitation pattern used by thenear-field large-angle algorithm. The fields produced at the sensorlocation in response to these excitation vectors are then: ##EQU6##

POSITION DETERMINATION

The output of a three-axis sensor of arbitrary orientation (ψ, θ, φ) isdetermined by applying orientation azimuth, elevation, and rollrotations to the output of the equivalent zero-orientation sensor, thus:##EQU7##

Since the sensor orientation is unknown at this point in the processing,use must be made of orientation-independent signal parameters. Threesuch parameters are:

1. Signal power, obtained by dot products by sensor response vectorswith themselves;

2. Dot products between different sensor response vectors, analogous tothe angles between the response vectors; and

3. The amplitudes of the cross products between different sensorresponses, analogous to the perpendiculars to the planes defined bythose responses.

Several algorithms are derived subsequently; the choice of algorithmdepends upon the application.

1. THREE-STATE POWER SOLUTION

The sensor responses from all three states of source excitationEquations (10), (11), and (12) can be converted to received power andprocessed to yield position in a manner similar to that used fornear-field applications. The three "power" responses are obtained bytaking dot products of the three sensor response vectors withthemselves. Since the sensor orientation is determined by a set oforthogonal rotations, the power is invariant under sensor rotation. Thethree power outputs are: ##EQU8##

Distance ρ is obtained from the sum of the three powers, which isindependent of α and β, thus the calculated distance ρ equals: ##EQU9##Rearrangement of Equation (16) then yields: ##EQU10## Substitution of ρand |β| into Equation (15) then produces: ##EQU11##

The position defined by α_(A), |β|, and ρ contains an eight quadrantambiguity (as in the near-field algorithm), which is reduced to atwo-quadrant ambiguity by the signs of the dot products. The threepossible dot-products are: ##EQU12##

Inspection of Table 3 shows that the polarities of any two of these dotproducts reduces the quadrant ambiguity from 8 to 2.

                                      TABLE 3                                     __________________________________________________________________________    Position Coordinates     Dot Products                                         Quadrant                                                                           x y  z α β                                                                             v(S1,S2)                                                                           v(S2,S3)                                                                           v(S3,S1)                                   __________________________________________________________________________    1    + +  - 0°...90°                                                                0°...+90°                                                            -    +    +                                          2    - +  - 90°...180°                                                              0°...+90°                                                            +    +    -                                          3    - -  - -90°...-180°                                                            0°...+90°                                                            -    -    -                                          4    + -  - 0°...-90°                                                               0°...+90°                                                            +    -    +                                          5    + +  + 0°...90°                                                                0°...-90°                                                            -    -    -                                          6    - +  + 90°...180°                                                              0°...-90°                                                            +    -    +                                          7    - -  - -90°...-180°                                                            0°...-90°                                                            -    +    +                                          8    + -  - 0°...90°                                                                0°...-90°                                                            +    +    -                                          __________________________________________________________________________

A somewhat more direct solution can be obtained if the power responsesare formulated in rectangular coordinates: First, ##EQU13## GeometricalSimilarity then requires that ##EQU14## and ##EQU15## Range ρ is firstfound by using Equation (17). Values of x², y², and z² are then found bysubstitution of measured "power" and ρ² into Equations (22), (24), and(25). FIG. 10 illustrates a flow diagram for the computations involvedin the implementation of a three-state power solution for position. FIG.10 also goes on to illustrate the flow diagram for the computationsinvolved in calculating orientation from the three-state power solutionfor position. The mathematical operations for calculating orientationare presented later.

2. TWO-STATE POWER AND DOT PRODUCT SOLUTION

A two-state large-angle algorithm similar to that for near-fieldoperation can be developed by using the normalization ##EQU16##Equations (24) and (25) then become:

    P(S1)=Y.sup.2 +Z.sup.2                                     (27)

and

    P(S2)=X.sup.2 +Z.sup.2                                     (28)

The first dot-product Equation (20) is then also converted to normalizedrectangular coordinates ##EQU17##

If the dot-product Equation (30) is zero, either X=0 or Y=0 or both;which of these is the case is readily determined by whetherP(S2) >P(S1), P(S1>P(S2) or P(S1)=P(S2), respectively. If v(S1,S2)≠0,then equation (30) can be rearranged into: ##EQU18## The difference of(28) and (27) then eliminates Z₁ :

    P(S2)-P(S1)=X.sup.2 -Y.sup.2                               , (32)

and substitution of Equation (31) produces an equation containing X² asthe only unknown: ##EQU19##

This new equation can be converted into a quadratic in X² and solved.The erroneous value of X² is then discarded and the correct value issubstituted into Equation (28) to determine Z². The value of Z² is thensubstituted into Equation (27) to determine Y². The sign of the dotproduct then reduces the quadrant ambiguity from 8 to 4. The 4 quadrantambiguity is eliminated by specifying particular parameters aspreviously discussed. FIG. 11 illustrates a flow diagram for thecomputations involved in the implementation of a two-state power and dotproduct solution for position. FIG. 11 also goes on to illustrate theflow diagram for the computations involved in calculating orientationfrom the two-state power and dot product solution for position. Themathematical operations for calculating orientation are presented later.

3. THREE-STATE CROSS-PRODUCT SOLUTION

The amplitude of the cross-product of two vectors is invariant under theorthogonal sensor orientation rotations and can therefore be used todetermine position independent of sensor orientation. The orientation ofthe cross product is, in an absolute sense, also invariant under sensororientation. However, the cross-product is referenced to the samecoordinate frame as are the vectors used to generate it. Therefore, thecross-product of two sensor responses is referenced to the sensorcoordinate frame. Since the orientation of the sensor is not known atthis point in the signal processing, little use can be made of theorientations of the cross products.

Inspection of the sensor-position-frame fields for the three axisexcitation states Equations (10), (11), and (12) shows that all havezero X components, which implies that both the Y and the Z components ofthe cross products of these vectors are zero. The resultantsensor-position-frame cross-product vectors are then ##EQU20##

These three cross products will be rotated by yet unknown sensororientation angles. However, the magnitudes of the cross-products (orthe squared magnitudes) are unchanged, hence we can obtain, independentof sensor orientation, ##EQU21## The solution for ρ, α₁, and β is ingeneral similar to the solutions by other methods. First: ##EQU22##Substitution of ρ into (38) then produces: ##EQU23## and the ratio of(40) to (39) gives ambiguous azimuth: ##EQU24## This position solutioncontains an eight-quadrant ambiguity that can be reduced to a twoquadrant ambiguity through the signs of the dot products as shown inTable 3.

4. TWO-STATE POWER AND CROSS-PRODUCT SOLUTION

It is evident that P(S1), P(S2), and Ξ (S1,S2) produce three equationsin the three unknown position parameters. To find position, firstrearrange Equation (38) to produce ##EQU25## Substitution of this intothe sum of Equations (14) and (15) leaves only ρ as an unknown:##EQU26## After ρ has been determined, |β| and α_(A) can be determinedin turn by substitutions into Equations (44) and (19), respectively.Quadrant ambiguity can be reduced from 8 to 4 by use of the sign ofv(S1,S2).

ORIENTATION DETERMINATION

Sensor orientation can be determined in a non-iterative manner from anytwo sensor output vectors corresponding to fields aligned with the souceaxes. These sensor output vectors are synthesized from the true sensoroutput vectors. One advantage of non-iterative orientation determinationover iterative orientation determination is an increase in processingspeed. Also, non-iterative orientation determination techniques are freefrom `latch up` and allow a reduction in software complexity.

The orientation rotations that convert the output of an equivalentzero-orientation sensor into the output of the true sensor 100 can becombined into a single matrix A, which can be expanded by using Table 1to produce: ##EQU27## Suppose that a source excitation produces aresponse f₄ (X)=[1, 0, 0]^(T) in a zero-orientation sensor (i.e. thefield at the sensor location has an X₁ -axis orientation. The outputfrom the real sensor 100 is then f₅ (X)=Af₄ (X)=[a₁₁, a₂₁, a₃₁ ]^(T),which is the first column of A. Similarly, the second and third columnsof A represent the sensor responses to fields of Y₁ -Z₁ -axisorientations, respectively.

If the normalized sensor output vectors corresponding to fields of X₁ -,Y₁ -, and Z₁ -axis orientations can be synthesized, the elements of Awill be known, and the angles ψ, θ, and φ can be determined. Forexample, using the sensor X-axis response to a field of Z₁ -axisorientation, ##EQU28## The angles ψ and φ can now be determined by usingthe just-determined value of θ to cancel the sin θ and cos θ factors inthe responses corresponding to a₁₁, a₁₂, a₂₃, and a₃₃.

Errors in the range estimate and variation in the source power produce amultiplicative error common to all sensor output vectors. The effects ofthose errors can be avoided by determining orientation from ratios ofsensor responses. Thus: ##EQU29## (Note that a four-quadrant inversetangent will place ψ and φ in the proper quadrant.) Elevation θ can bedetermined from ##EQU30## or three similar ratios using a₁₃, and a₁₂,a₂₃, or a₃₃. A linear combination of all four ratios can also be used tominimize the effects of noise.

While orientation is most simply determined using elements from allthree synthetic sensor output vectors, inspection of the matrix A inEquation (46) shows that the information contained in any two columns issufficient to determine all three orientation angles. Some flexibilityis therefore possible in a noisy environment; e.g., orientation can beestimated from the two output vectors with minimum estimated noise.Alternatively, information from all three output vectors might becombined by linearizing the elements of A about the initial orientationestimates from Equations (48), (49), and (50). Minimum-variance linearcombinations would then be formed to improve the initial estimates.

NEAR-FIELD CONDITIONS, THREE-STATE EXCITATION

Fields of X₁ -, Y₁ -, and Z₁ -axis orientations are produced at thesensor location only when the sensor 100 is located on the X₁, Y₁, or Z₁axis. The source excitation pattern is fixed to allow multiple sensorsto derive position and orientation information from the same signals. Ina near-field system with a three-state source-excitation pattern (U.S.Pat. No. 4,054,881), the responses of the sensor to fields of X₁, Y₁,and Z₁ -axis orientations can be synthesized from the real sensorresponses, which span three-dimensional vector space.

The three true sensor output vectors can be assembled into a 3×3 matrixF₅, which can then be written as: ##EQU31## From the above equation, itis evident that the desired matrix A of synthetic responses can beobtained as: ##EQU32## The coupling matrix Q⁻¹ is computed usingestimated values α and β. Note that actual matrix inversion isunnecessary, since ##EQU33##

FAR-FIELD CONDITIONS, THREE-OR TWO-STATE EXCITATION

While all orientation information is contained in any two sensor outputvectors, synthesis of the desired sensor responses (i.e., the matrix A)requires a three-dimensional set of basis vectors. However, underfar-field coupling conditions, the coupling matrix S (Equation (3)) isdegenerate (rank 2). Therefore, the inverses S⁻¹, hence Q⁻¹, (Equations(53) and (54)) do not exist and Equation (52) cannot be used directly tosynthesize orientation matrix A.

The orientation matrix A can, however, be synthesized by using the crossproduct of two non-colinear sensor output vectors to provide thenecessary third linearly independent vector. Suppose that the responsesto state S1 and state S2 excitation are available and since orthogonalrotations preserve the angles between vectors, ##EQU34##

The cross products can be used in place of the vectors produced by thethird excitation state in forming the matrices F₅ and F₄, thus ##EQU35##The vectors f₄ (S1) and f₄ (S2), and hence f₄ (CP) can be calculatedfrom the estimated position. The vector f₅ (CP) can be calculated fromthe two sensor output vectors. The estimated orientation matrix A canthen be determined from: ##EQU36## Orientation angles are thendetermined as discussed previously. For computational convenience, itmay be desirable to multiply f₅ (S1), f₅ (S2), f₄ (S1), and f₄ (S2) byρ/C before computing the cross products; this results in cross-productvectors and sensor output vectors having roughly the same magnitude.

Matrix inversion can be avoided by an alternative method of determiningorientation. Linear combinations of the two field vectors at the sensorlocation form two orthogonal synthetic field vectors; application of thesame coefficients to the two sensor output vectors produces theanalogous synthetic response vectors.

The two synthetic sensor response vectors are placed in the second andthird columns of a matrix A', and orientation angles ψ', θ', and φ' aredetermined from those two columns. Those orientation angles are definedin the same manner as are ψ, θ, and φ, but are referenced to the Y.'-Z'coordinate frame formed by the two synthetic field vectors. Theorientation (α', β', θ') of the Y'-Z axes with respect to the X₁ -Y₁ -Z₁axes is then determined by multiplying direction cosine vectors. Thematrix A whose orientation angles are reference to the X₁ -Y₁ -Z₁coordinate frame is then: ##EQU37## This method may allow a reduction ofcomputation time in some applications.

If the sensor lies in the X₁ -Y₁ plane, two sensor outputs will becolinear, and orientation cannot be determined from f₅ (S1) and f₅ (S2)alone. This suggests that for the most general allowable orientations,three-state operation should be used so that there will always be somebasis against which orientation can be determined.

In far-field operation, the cross-product of any two field vectors atthe sensor location is oriented radially away from the source, seeEquations (35), (36), and (37). Transmission of such a vector isphysically impossible, hence the cross-product is not a directsubstitute for the third-axis (S3) excitation.

The cross-product is nonetheless useful in determining large-angleorientation for far-field operation. Linear combinations of the two realsensor responses and their cross product can produce synthetic responsesto non-physically realizable source-frame Y₁ - and Z₁ -oriented fields.The synthetic responses g₅ (S2) and g₅ (S3) thus determined then yieldsource-frame orientation angles when used in the large-angle orientationalgorithms. The coefficients required to implement the two lineartransformations are elements of the inverse of a matrix composed of thetwo computed field vectors [f₄ (S1) and f₄ (S2)] and their cross productf₄ (CP).

It should be noted that the equations which have been derived in thepresent disclosure are based upon electromagnetic fields generated byelectrically short (0.1λ or shorter) dipoles. Longer dipoles and arrayshave different field patterns that will make these equations invalid. Ifsuch antennas are to be used, appropriate equations should be derived.

POSITION OF SOURCE OF UNKNOWN ORIENTATION

Three-axis reception of the signals from a multi-axis source providesinformation adequate to determine the position angles of the sourcerelative to the sensor, even when the source orientation is unknown orthe source structure is unknown. Note that this method of determiningthe direction of arrival of a signal differs from that used by ordinarydirection finding, which rotates an antenna until a null in the antennapattern is aligned with the direction of arrival, thus nulling thereceived signal.

Examination of the above field-coupling equations shows that the sensoroutput vector f₅ is related to the position-frame source-excitationvector f₂ by ##EQU38## note that the above position (α,β) andorientation angles (ψ, θ, φ) are referenced to the source coordinateframe.

Since both T_(A) and T_(P) ⁻¹ are composed entirely of orthogonalrotations, their product can be reduced to a product of no more thanthree simple rotation matrices. Since the location of the source 98 withregard to the sensor coordinate frame is desired, it is convenient touse the sensor-frame position angles α' and β' and a roll rotation byγ', which are shown in FIG. 9. Equation 59 then becomes ##EQU39##

Now consider the characteristics of a sensor position-frame vector f₃and the cross product f₃ (CP) of two sensor position-frame vectors. FromEquation (60), ##EQU40## since f_(3X) =O, it is apparent that f₃ isorthogonal to the line connecting source 98 and the sensor 100.Furthermore, ##EQU41## Unless f_(3X) (CP)=0 (which occurs only when f₃(S1) and f₃ (S2) are colinear), f₃ (CP) is aligned with (parallel to)the line connecting the source 98 and sensor 100. Note that it may bedirected either toward the source 98 or toward the sensor 100.

Since orthogonal rotations preserve the angles between vectors, as wellas vector length, the cross product f₅ (CP) of two sensor output vectorsis easily related to the cross product of the two sensor position-frameoutput vectors: ##EQU42## Since a roll rotation has no effect on theX-element in a vector, and f_(3y) (CP)=f_(3Z) (CP)=0, f₃ (CP) isinvariant under T₋γ' and ##EQU43##

Carrying out the matrix multiplications in (66) produces: ##EQU44## Theunknown angles α' and β' can then be determined from f₅ (CP) in severalways; for example, ##EQU45## If C and f_(3X) (CP) are known, the unknowndistance ρ can be determined. Alternatively, if the source 98 has threeorthogonal axes, Equation (17) can be used to determine ρ. Remember thatf₅ (CP) is determined entirely from measured sensor output vectors withno a priori information about the source 98.

SIGNAL FORMATS

The signal format used by the transmitter must be designed to allow theuser to determine his position and orientation. The geometriccomputations discussed in the previous section establish someinformational parameters which are advantageously met by the format.First, it must allow airborne components 20 to determine the amplitudeof the signal induced in a given receiving antenna (22, 23 or 24) byeach transmitting antenna (41, 42 or 43). Secondly, it advantageouslyprovides one-way data transmission capability so airborne components 20will know the power, (i.e. strengths), of the transmitted signal.Thirdly, to facilitate communication of both of the previous informationparameters, the signal may include a timing reference, and all signalcomponents should advantageously be coherent with this reference. Thetiming signal is used to characterize the polarity of the transmittedsignal. If this timing signal is omitted, there is an increase in theambiguity as to position and orientation of the remote object. Ofcourse, independent information sources may be used to remove thisambiguity. For example, navigation aids may be used to determine thequadrant (i.e. northeast, southeast, northwest or southwest) of theremote object with respect to the radiating means; altimeters may beused to determine the relative height of the remote object with respectto the radiating means, which may be located at the top of the hill.

There are endless varieties of formats which can meet the aboverequirements. However, it is additionally desirable that the signalformat allow easy acquisition by the user as he approaches the landingpoint. Simplicity in the receiver is also quite desirable. Fourpossibilities for transmitted signal format are:

1. FREQUENCY DIVISION MULTIPLEXING (FDM)

In this format, each transmitting antenna in the array is assigned aparticular, different frequency. Measurements of the informationparameters can be simply the outputs of integrators corresponding to thethree frequencies. The carriers are of constant phase and thereforeeasily acquired by a phase-locked loop with an appropriate timeconstant.

2. TIME DIVISION MULTIPLEXING (TDM)

In TDM, only one dipole of the ground antenna array is excited at atime. Simplification of transmitter and receiver is possible becausecircuits can be time-shared. However, data transmission is more complex,and moving aircraft must interpolate between measurements to provide theequivalent of simultaneous measurements. This is an advantageous mode ofmultiplexing for the location of a relatively slow moving or trappedminer below ground.

3. PHASE DIVISION MULTIPLEXING (nutation)

Proper excitation of the three dipoles will produce the equivalent ofphysical nutation of a single dipole antenna. This may be accomplishedby excitation of the Z dipole with an unmodulated carrier and the X andY dipoles by carriers with high frequency amplitude modulation by sineand cosine waves, respectively. While this results in a beacon-likesignal, that property is not actually utilized in the position andorientation calculations. What is utilized is that the radiatedelectromagnetic field from each of the ground dipole antennas can beidentified by either an unmodulated carrier or a phase differencebetween the modulation envelope of two modulated carriers. If a nutatingfield is used there is no requirement that the axis of nutation bepositioned along a line between the radiating and the receivingantennas. The position and orientation of the remote object can bedetermined regardless of the orientation of the axis of nutation.

4. SPREAD SPECTRUM MULTIPLEXING

To accomplish spread spectrum multiplexing, each transmitted signal isassigned a unique code sequence which shifts carrier frequency, carrierphase (or both). Reception is accomplished by using identical codesequences to remove the modulation. The codes assigned to the threeantennas are designed not to cross correlate and thus make possiblemeasurement of individual signals. However, acquisition is typicallymore difficult, both because of the absence of a carrier component andbecause the code timing must be acquired, in addition to the carrier.

The selection of carrier frequency, spread-spectrum chipping rate, datafrequency, transmitter power, antenna size, and other parameters isnaturally dependent upon this application. Carrier frequencies in the200 to 3000 MHz range will generally be found suitable. For thesecarrier frequencies, chipping rates of 100 kHz to 10 MHz are practical.Consequently, data frequencies of 10 kb/s to 1 Mb/s are possible. Iffrequency-division multiplex is used, carrier frequencies should beseparated by 10 kHz to 100 kHz to allow for Doppler shifts.

While the present invention has been described in terms of a longdistance landing aid system, it can also be useful in applications suchas airdrop guidance and control, collision avoidance, target handoff,and refueling and station keeping.

Various modifications and variations will no doubt occur to thoseskilled in the various arts to which this invention pertains. Asdiscussed above, the signal format may be chosen from any of numerousalternatives. Additionally, the particular parameters of thetransmitting and receiving apparatus will depend upon the particularapplication. Systems for either longer or shorter ranges can be designedby appropriate choices of parameters. These and all other variationswhich rely basically on the teachings through which this disclosure hasadvanced the art are properly considered within the scope of thisinvention as defined by the appended claims.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined as follows:
 1. Apparatus fordetermining the position of a source of electromagnetic radiationrelative to a remote object and the orientation of the remote objectrelative to the position of the source comprising:a multicomponentradiating means of unknown orientation and structure identifying theorigin of said source; transmitter means for applying to saidmulticomponent radiating means electrical signals which generate aplurality of electromagnetic fields, said plurality of electromagneticfields being distinguishable from one another; a plurality of receivingmeans disposed on said remote object, said receiving means having atleast three orthogonal components for detecting and measuring componentsof said electromagnetic fields; said radiating means and said receivingmeans being adapted for operation at a separation distance sufficient toinsure that the far-field components of said electromagnetic fields aresubstantially greater in magnitude than the near-field components ofsaid electromagnetic fields; and analyzing means associated with saidreceiving means for converting the components of said electromagneticfields received by said plurality of receiving means into sourceposition relative to said remote object without a priori knowledge ofthe orientation of said source or the relative orientation of itscomponents with at least one ambiguous combination of orientation orposition, said analyzing means comprising means for operating open loopwith respect to said radiating means.
 2. Apparatus as recited in claim 1wherein said transmitting means comprises at least two orthogonalcomponents.
 3. Apparatus as recited in claim 2 wherein said analyzingmeans comprises means for converting, in a non-iterative manner, thecomponents of said electromagnetic fields received by said receivingmeans into remote object position and orientation relative to saidsource.
 4. Apparatus as recited in claim 1 wherein said transmittingmeans comprises three orthogonal components.
 5. Apparatus as recited inclaim 1 wherein said transmitter means comprises means for multiplexing,said means for multiplexing being selected from a group of circuitsincluding circuits for time, frequency, phase and spread spectrummultiplexing of said electrical signals.
 6. Apparatus as recited inclaim 1 wherein said analyzing means is physically remote from saidreceiving means and said analyzing means and said receiving means arecoupled by electromagnetic radiation.
 7. Apparatus as recited in claim 1wherein each of said radiating means comprises an electric dipolesource.
 8. Apparatus as recited in claim 1 wherein said transmittermeans comprises means for generating electrical signals containinginformation selected from the group of transmitter identification,electromagnetic field distortion corrections, locations of obstacles,location of a landing site relative to said radiating means and winddirection.
 9. Apparatus as recited in claim 1 comprising a monitorstation at a fixed location spaced from said radiating means havingreceiving means for detecting said radiated electromagnetic fields andbeing coupled to said transmitting means for providing feedback to saidtransmitting means representative of said transmitted fields.